Organized by Sergei Gukov, Nuno Romao, and Samson Shatashvili
Dates: November 3 – 7, 2014
Attendee ListDownload Talk ScheduleView Videos
Download Transportation ScheduleGauged Sigma-Models in Two Dimensions
| Time | Title | Presenters | Video |
| 8:30am | Breakfast | SCGP Cafe | |
| 9:30am | Registration | SCGP Lobby | |
| 10:45am | Welcome | ||
| 11:00am | Bethe wavefunctions from gauged linear sigma models via Bethe/gauge correspondence | Nikita Nekrasov | video |
| 12:00pm | Lunch | SCGP Cafe | |
| 2:00pm | Microscopic GLSM Description of M2-brane Surface Operators and Sphere Partition Functions | Jaume Gomis | video slides |
| 3:00pm | A quasi-topological gauged sigma model, the geometric Langlands program, and knots | Meng-Chwan Tan | video slides |
| 4:00pm | Tea Time | ||
| 4:45pm | Gravitating vortices | Oscar Garcia-Prada | video slides |
| Time | Title | Presenters | Video |
| 8:30am | Breakfast | SCGP Cafe | |
| 9:30am | Nonlinear vortices on nearly nodal curves | Ignasi Mundet i Riera | video |
| 10:30am | Coffee Break | SCGP Cafe | |
| 11:00am | The L^2 geometry of the space of P^1 vortex-antivortex pairs | Martin Speight | video slides |
| 12:00pm | Lunch | SCGP Cafe | |
| 1:00pm | SCGP Weekly Talk: Vortex Equations and Invariants: A Survey | Ignasi Mundet i Riera | video |
| 2:00pm | Divisor Links | Marcel Bokstedt | video |
| 3:00pm | L^2-Betti Numbers and Particle Counting in a Gauged Nonlinear Sigma-Model | Christian Wegner | video |
| 4:00pm | Tea Time | ||
| 4:45pm | Gauged Witten Equation and Correlation Functions | Guangbo Xu | video |
| Time | Title | Presenters | Video |
| 8:30am | Breakfast | SCGP Cafe | |
| 9:30am | The Verlinde algebra and its generalisations | Anton Kapustin | video |
| 10:30am | Coffee Break | SCGP Cafe | |
| 11:00am | Chiral rings in 2d (0,2) theories | Eric Sharpe | video slides |
| 12:00pm | Lunch | SCGP Cafe | |
| 2:00pm | Exact solutions of 2d supersymmetric gauge theories | Abhijit Gadde | video slides |
| 3:00pm | Branes and vortices | Amihay Hanany | video |
| 4:00pm | Tea Time | ||
| 5:00pm | Art Event: Wine and Cheese Reception | SCGP Lobby | |
| 5:30pm | Art Talk: Colliding Worlds: How Cutting-Edge Science is Redefining Contemporary Art | Arthur Miller |
| Time | Title | Presenters | Video |
| 8:30am | Breakfast | SCGP Cafe | |
| 9:30am | Mirror Symmetry and Gauged Linear Sigma Models | Dave Morrison | video |
| 10:30am | Coffe Break | SCGP Cafe | |
| 11:00am | Flipping out over vortices | Chris Woodward | video slides |
| 12:00pm | Lunch | SCGP Cafe | |
| 2:00pm | Grade Restriction Rule for Rodland Model and Pfaffian/Grassmann Correspondence, via Hemisphere Partition Function | Kentaro Hori | videoUpdate |
| 3:00pm | Cluster Algebras from 2d Gauge Theories | Francesco Benini | video slides |
| 4:00pm | Tea Time | ||
| 6:00pm | Workshop Banquet |
| Time | Title | Presenters | Video |
| 8:30am | Breakfast | SCGP Cafe | |
| 9:30am | 3d N=4 Gauge Theory and Symplectic Duality | Tudor Dimofte | video |
| 10:30am | Coffee Break | SCGP Cafe | |
| 11:00am | Superconformal index and surface defects | Lotte Hollands | video |
| 12:00pm | Lunch | SCGP Cafe | |
| 2:00pm | BPS States, Knots, and Vortices | Piotr Sulkowski | No Video |
| 3:00pm | Equivariant Integration Over Hitchin Moduli Space | Du Pei | video |
| 4:00pm | Tea Time |
Gauged sigma-models from Riemann surfaces to Kaehler targets have been an important ingredient in recent developments at the crossroads of quantum field theory, geometry and topology. Of particular interest are models that exhibit self-duality, since they are more amenable to rigorous treatment — they incorporate a rich mathematical structure reflecting the fact that they admit certain local extensions accommodating representations of the N=(2,2) supersymmetry algebra. Twisted versions of these supersymmetric models yield topological quantum field theories that are defined on arbitrary Riemann surfaces. The correlators of such theories are formally expressed through path integrals, but they localize to finite-dimensional integrals which have a rigorous formulation. The TQFTs obtained via an A-twist localize to the moduli space of solutions to the vortex equations, whose quantum observables are intimately related to gauged Gromov-Witten invariants constructed from the action on the target manifold. They realize the quantum equivariant cohomology ring of the group action on the target, in a generalization of the familiar framework for Gromov-Witten theory for pseudo-holomorphic maps from a complex curve to a symplectic manifold. When the target of the sigma-model is an equivariant Calabi-Yau manifold, one can also produce an alternative B-twist, whose correlators localize to the Kaehler quotient of the target. The potential of studying two-dimensional self-dual gauged sigma-models has already been vindicated by a number of recent breakthroughs, which we intend to showcase in this workshop.
This workshop is a part of the Fall 2014 program, Gauge Theory, Integrability, and Novel Symmetries of Quantum Field Theory, which is organized by Anton Kapustin, Nikita Nekrasov, Samson Shatashvili, Volker Schomerus, and Konstantin Zarembo. This program takes place from September 2 – December 19, 2014.
